Q. 1 K5.0( 2 Votes )

# Find the interval

Answer :

Given:- Function f(x) = 2x3 – 9x2 + 12x – 5

Theorem:- Let f be a differentiable real function defined on an open interval (a,b).

(i) If f’(x) > 0 for all , then f(x) is increasing on (a, b)

(ii) If f’(x) < 0 for all , then f(x) is decreasing on (a, b)

Algorithm:-

(i) Obtain the function and put it equal to f(x)

(ii) Find f’(x)

(iii) Put f’(x) > 0 and solve this inequation.

For the value of x obtained in (ii) f(x) is increasing and for remaining points in its domain it is decreasing.

Here we have,

f(x) = 2x3 – 9x2 + 12x – 5 f’(x) = 6x2 – 18x + 12

For f(x) lets find critical point, we must have

f’(x) = 0

6x2 – 18x + 12 = 0

6(x2 – 3x + 2) = 0

6(x2 – 2x – x + 2) = 0

x2 – 2x – x + 2 = 0

(x – 2)(x – 1) = 0

x = 1, 2

clearly, f’(x) > 0 if x < 1 and x > 2

and f’(x) < 0 if 1 < x < 2

Thus, f(x) increases on (–, 1) (2, ∞)

and f(x) is decreasing on interval x (1,2)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Show that the altMathematics - Board Papers

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1

Find the intervalRD Sharma - Volume 1